Problem

If n=24,x¯=34, and s=6, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.
Can we conclude that the population mean is at least 29.04?
No
Yes

Can we conclude that the population mean is no more than 38.56 ?
No
Yes
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Answer

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Answer

Can we conclude that the population mean is no more than 38.56? Yes, because 38.56 is greater than the upper limit of our confidence interval.

Steps

Step 1 :Given: n=24, x¯=34, s=6, and a 98% confidence level.

Step 2 :The Z-score for a 98% confidence level is approximately 2.33 (you can find this value in a standard Z-table).

Step 3 :Substitute these values into the formula for the confidence interval: CI=x¯±Z(s/n)

Step 4 :Calculate the value inside the parentheses: 6/24=1.224744871

Step 5 :Multiply this by the Z-score: 2.331.224744871=2.85365347

Step 6 :So, the confidence interval is: CI=34±2.85365347

Step 7 :This gives us a range from: 342.85365347=31.1463465331.1 (to one decimal place)

Step 8 :to: 34+2.85365347=36.8536534736.9 (to one decimal place)

Step 9 :So, the 98% confidence interval is (31.1,36.9)

Step 10 :Can we conclude that the population mean is at least 29.04? No, because 29.04 is not within our confidence interval.

Step 11 :Can we conclude that the population mean is no more than 38.56? Yes, because 38.56 is greater than the upper limit of our confidence interval.

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